A projected Weiszfeld algorithm for the box-constrained Weber location problem

ELVIO ANGEL PILOTTA; GERMÁN ARIEL TORRES

APPLIED MATHEMATICS AND COMPUTATION

ELSEVIER SCIENCE INC

Año: 2011 vol. 218 p. 2932 - 2943

0096-3003

The Weber problem consists of finding a point that minimizes the weighted sum of distances from m points that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the Weber problem, proposed by Weiszfeld in 1937, is based on a fixed-point iteration. In this work we generalize the Weber location problem considering box constraints. We propose a fixed-point iteration with projections on the constraints and demonstrate descending properties. It is also proved that the limit of the sequence generated by the method is a feasible point and satisfiesthe KKT optimality conditions. Numerical experiments are presented to validate the theoretical results.